In this chapter, you will learn:
• What a polynomial is
• Add/subtract/multiply/divide polynomials
• Simplify radicals, exponents
• Solving equations with exponents and radicals
• Complex numbers
• Conjugates
What is a monomial?
An expression that is a number, that may or may not include a variable.
x4
2x2xy10
MONOMIALS NOT MONOMIALS
x
48x
x518
Real Roots• Real roots are the
possible solutions to a number, raised to a power.
powerfourth the to16 of roots
are 2 negative and 2both so
16)2(2 44
5?) beit t can'(why
125- ofroot real
possibleonly theis 5- so
12553
power
second the x toof roots
arex - andboth x so
2
xxor
xxx
How to find the root (other than a square
root), using a graphing calculator 1. Input the root you are going to
take (for example, if you are taking the third root of a number, start with the 3).
2.Press MATH and select option 5
3. Enter the value you are taking the root of.
Ex:
x
4 81 4 MATH 5 81 ENTER
3
Practice: Find each root
3 10648
5 16807
Solutions: 22, 7, and
ERR: NONREAL ANS
4 16Let’s take a closer look at this answer
Properties and Notation:
aan When n is an even number
Why? We want to make sure that the root is always positive when the index is an even number
positive. stays
it sure make to valueabsolute theuse Weforwards. and
backwards trueisit that so indexeseven with
positive a always is that x sure make want to we
525)5(,5 if BUT
5255,5 IF
:itat look y toanother wa sHere'
22
22
so
xxx
xxx
24 42444 84 2)()2(16
:
yxyxyx
ex
Note: Absolute value symbols ensure that the root is positive when x is negative. They are not needed for y because y2 is never negative.
23 3233 63 )(
:
yxyxyx
ex
Absolute value symbols must not be used here. If x is negative, then the radicand is negative and the root must also be negative.
Notice that the index is an odd number here . . .
Let’s try some
3 627 yx
Simplify each expression. Use the absolute value symbols when needed.
424 yx
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